CrimsonScythe

Just like the real Alessa,Dark alessa likely to share the same
power,but Dark Alessa seems like own her own individual ability
that don't owned by the real Alessa

Here is the information Im able to analize from them

Possesion : When Dark Alessa hug Rose in the
hospital,she able to merge with her,and when Christabella stab
Rose,she spilled "black blood" that seems like the essence of Dark
Alessa

Able to appear and dissapear anytime : Dark Alessa
use this ability to run through Silent hill and lure Rose to
certain places. In the Hospital room where Alessa gillespie take
rest,Dark Alessa just appear near The red nurse (Lisa Garland),even
though Rose already check that corner before. Dark Alessa clearly
show this ability when confronting Heather …